Suppose the solid cylinder in the apparatus described in Example 9.8 (Section 9.4) is replaced by a
Question:
Suppose the solid cylinder in the apparatus described in Example 9.8 (Section 9.4) is replaced by a thin-walled, hollow cylinder with the same mass M and radius R. The cylinder is attached to the axle by spokes of a negligible moment of inertia.
(a) Find the speed of the hanging mass m just as it strikes the floor.
(b) Use energy concepts to explain why the answer to part (a) is different from the speed found in Example 9.8.
In Example 9.8:
We wrap a light, non stretching cable around a solid cylinder with mass M and radius R. The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass m and release the block from rest at a distance h above the floor. As the block falls, the cable unwinds without stretching or slipping. Find expressions for the speed of the falling block and the angular speed of the cylinder as the block strikes the floor.
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Identify Repeat the calculation in Example 98 but with a different expre...View the full answer
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Skateboarding is a fun and popular activity among young people, in which the participant stands on a small board with wheels and navigates different surfaces. It is considered an extreme sport and there are professional competitions for different disciplines like vertical and street skating. To start skateboarding, focus on maintaining balance and having fun. To control the board, use your feet and keep your body\'s center of mass over the skateboard. The most stable and safest riding position is to have your front foot just behind or on the front bolts of the board and your back foot close to the back of the board, near or on the heel. This position also makes quick kick turns easier. Once you have mastered the basics, you can learn various tricks to impress others.
In terms of mechanics, skateboarding involves the principles of force and torque. The rider exerts force on the skateboard to make it move, and torque is used to turn the board or perform tricks. Friction between the wheels and the ground also plays an important role in allowing the rider to control the speed and direction of the board. Energy is also involved in skateboarding, specifically the transfer of potential energy to kinetic energy. When a rider jumps on a skateboard, they transfer potential energy stored in their muscles into kinetic energy, which propels the board forward. The rider can also transfer kinetic energy into potential energy by performing an aerial trick and then landing back on the board.
